SDF troops, led by Kurdish fighters, have been holding out for the past 10 days.
Mustafa Bali, head of the SDF media office, did not indicate how soon he expected the civilian evacuation to be completed.
The SDF, backed by United States air power, has driven Isis from large swaths of territory it once controlled in northern and eastern Syria, confining the extremists to a small pocket of land near the border with Iraq.
"After ten days of evacuating more than 20,000 civilians. the battle was launched tonight to exterminate the last remnants of the organisation".
Earlier in the day, a war monitor reported that negotiations are underway in eastern Syria between the USA -led forces and the IS group for the latter's withdrawal from its last redoubt.
"They are attempting to escape through intermixing with the innocent women and children attempting to flee the fighting", coalition deputy commander Christopher Ghika said on Thursday.More news: Senate panel approves Trump's attorney general nominee
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Unless the Trump administration alters course, the military plans to pull a significant portion of its 2,000 troops out by the middle of next month, with a full withdrawal coming by the end of April, the newspaper said on Wednesday.
Kurdish authorities say they have in their custody hundreds of foreign male IS members.
Thousands of suspected ISIS fighters have attempted to blend in with civilians fleeing the jihadists' last bastion, including a large number of foreigners.
The country's Kurds have largely stayed out of the conflict, instead developing semi-autonomous institutions in parts of the country's northeast under their control.
Special Operations forces working alongside the SDF fighters will be particularly keen on establishing whether any key Islamic State leaders are still holed up in Baghouz, including perhaps the Islamic State's leader, Abu Bakr al-Baghdadi. U.S.
US and SDF officials say, however, they have no reason to believe he is there.
"We are not discussing the timeline of the U.S".
"ISIS remains an active insurgent group in both Iraq and Syria", noted a report last week by the Pentagon's Inspector General.